What is the ratio of frac{q}{m} for an alpha- | vedclass

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(C) The charge of an $\alpha$-particle is $q_{\alpha} = 2e$ and its mass is $m_{\alpha} = 4m_p$,where $e$ is the elementary charge and $m_p$ is the ma

Vedclass · Accepted Answer

$1:2$

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(C) The charge of an $\alpha$-particle is $q_{\alpha} = 2e$ and its mass is $m_{\alpha} = 4m_p$,where $e$ is the elementary charge and $m_p$ is the mass of a proton.For a proton,the charge is $q_p = e$ and the mass is $m_p$.The ratio of specific charge $\frac{q}{m}$ for an $\alpha$-particle is $(\frac{q}{m})_{\alpha} = \frac{2e}{4m_p} = \frac{1}{2} \frac{e}{m_p}$.The ratio of specific charge for a proton is $(\frac{q}{m})_p = \frac{e}{m_p}$.Therefore,the ratio of $\frac{q}{m}$ for an $\alpha$-particle to that of a proton is $\frac{(\frac{q}{m})_{\alpha}}{(\frac{q}{m})_p} = \frac{\frac{1}{2} \frac{e}{m_p}}{\frac{e}{m_p}} = \frac{1}{2}$.

What is the ratio of $\frac{q}{m}$ for an $\alpha$-particle to that of a proton?

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